As far as I understand, rewards of pool mining are devided by the miners of the pool. So I will get 1 XMR with 1 KH/sec in about 1 week, if I start mining now.
That's right. But if you solo-mine, it could become 3 days or 2 weeks, depending on nothing but luck. With a pool, you're almost guaranteed to accumulate 1 XMR at the end of the week, when you add up all partial rewards you earn from mining on the pool.
If I do solo mining, it will take longer to find a block. But in the long term, I should get the same reward, since I will also find blocks. It will only take longer to find the next block.
In principle, over long term, it should be the same. In practice there could be some difference due to variances in network hashrate and difficulty while you're attemting to solo-mine a block.
That's why pools exist, to remove variance from mining. Joining a smaller pool which finds 1-2 blocks daily would give you a similar experience to solo mining but with less wait period between 2 rewards.
Joining a bigger pool would give you a more-less continous stream of rewards as they usually find more than a block per hour.
General advice is to join a smaller pool to help decentralization. Also, as it's exposed to some variance, so you could get lucky ;)
For miners who have such hashrate which lets them find a block in 1-2 days, solo mining is probably the better option as you mine directly to your address and don't pay any fees in the process.